In many secure communication systems known to those skilled in the art, a key, or series of keys, are processed according to a given algorithm with a plain text to produce an encrypted text. It is assumed that the algorithm is well known. Thus, the security of the encrypted text is dependent on the security of the key.
It follows that the secure transmission of the key, from the party encrypting the plain text to the party decrypting the encrypted text, is of great importance. In many cases, the key is sent by means other than those used to send the encrypted text. Alternatively, the key itself is not transmitted, but some signal is transmitted by the encrypting party that allows for the remote generation of the key by the decrypting party. Chaotic systems can be used for the remote generation of a digital key.
In general, a chaotic system is a dynamical system which has no periodicity and the final state of which depends so sensitively on the system's precise initial state that its time-dependent path is, in effect, long-term unpredictable even though it is deterministic. Identical chaotic systems can be distributed in a secure manner to an encrypting party and a decrypting party. When the encrypting party desires to communicate a digital key to the decrypting party, a number of different systems can be used to cause the digital key to be generated remotely by the decrypting party without transmitting the digital key itself.
In one method, described in Short, et al—Method and Apparatus for Secure Digital Chaotic Communication—application Ser. No. 09/436,910 filed Nov. 9, 1999 and incorporated herein by reference (“Short et al.—Chaotic Communication”), a bitstream is selected by the encrypting party for use as a digital key and is then generated remotely by the decrypting party. Controls are intermittently applied by a transmitter-encoder to a chaotic system to generate a bitstream corresponding to the digital key. A control/no control bitstream is thereby created in which a 0 indicates that no control was applied and a 1 indicates that a control was applied. The control/no control bitstream and a prepended synchronization bitstream are transmitted to a receiver-decoder. An identical chaotic system in the receiver-decoder is driven into synchrony and is then subject to intermittent controls based on the control/no control bitstream, thereby causing the identical chaotic system to generate the digital key.
The method of the present invention does not start with the selection of a bitstream for use as a digital key. Instead, a chaotic system in an encryptor is allowed to generate an unpredictable bitstream, for use as a digital key, which bitstream is then also generated remotely at an identical chaotic system in a decryptor. An initialization code is sent by an encryptor to a chaotic system, which is then allowed to generate an unpredictable key bitstream. The same initialization code is sent to an identical chaotic system in a decryptor to drive that chaotic system into synchrony. The synchronized chaotic system is then allowed to generate a key bitstream, which is identical to the other key bitstream because the chaotic systems have been synchronized. The initialization code, if it is intercepted, cannot be used to reproduce either the key bitstream or the chaotic system.